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This part of the help manual will try to give a small introduction to the theory of the kinematics and kinetics of the lower extremety.

Mathematical model

The joint angle definition is based on Grood and Suntay (1983) which uses traditional anatomical joint angles (flexion/extention, abduction/adduction and internal/external rotation).

When calculating net joint moments, a ridgid free body diagram is used.

Using Newtonian rules the following mathematical model can be obtained:


When estimating body segment parameters (mass, center of mass, moments of initia) it is important to normalize between subjects. The following measurement are needed:
bulletbody mass
bulletASIS breath
bulletMeasured from the to the
bulletThigh length
bulletMidthigh circumference
bulletCalf length
bulletCalf circumference
bulletKnee diameter
bulletFoot length
bulletMalleolus height
bulletMalleolus width
bulletFoot breadth

More accurate description of the measurements must be supplied!

Body markers

Determining segment orientation in 3D space requires at least 3 markers. The marker setup used in the 3Dkin is a 15 marker configuration for a analysis of both legs:
bulletMarker # 1 - Right metatarsal V
bulletMarker # 2 - Right heel
bulletMarker # 3 - Right lateral malleolus
bulletMarker # 4 - Right tibial tubercle
bulletMarker # 5 - Right femoral epicondyl
bulletMarker # 6 - Right greater trochanter
bulletMarker # 7 - Right anterior superior iliac spine
bulletMarker # 8 - Left metatarsal V
bulletMarker # 9 - Left heel
bulletMarker # 10 - Left lateral malleolus
bulletMarker # 11 - Left tibial tubercle
bulletMarker # 12 - Left femoral epicondyl
bulletMarker # 13 - Left greater trochanter
bulletMarker # 14 - Left anterior superior iliac spine
bulletMarker # 15 - Sacrum

It is important for the 3Dkin that the marker configuration is exactly as shown, despite that only one leg is calculated. If only one leg is analysed the markers not used can in the digitizing process be configured as missing.

Forceplate markers

Locating the forceplate in respect to the subject a marker must be mounted in one of the four corners of the forceplate. If 2 plates are used, it is possible to use the setup from the APAS analog file to locate forceplate #2 with respect to forceplate #1. If this option is not to be used, a second marker must be placed on the second forceplate. The forceplate markers must be configured as following:
bulletMarker # 16 - Forceplate # 1
bulletMarker # 17 - Forceplate # 2

Marker size consideration

Many things influence the choice of reflective marker size like room light, background color, subject color, floor color and so on. If more than two views are used the option of auto digitizing in the 3DKin.exe program must be considered. The success of auto digitizing is crucial to the choice of reflective marker size. The best way of choosing the optimal reflective marker size is to experiment with various types and sizes and also to modify the room color, light, and maybe using thin dark pants for the subject.

Joint center calculation

The joint center is calculated using a local coordinate system created from the body markers. Using three parameters (Uv,Uu,Uw) representing the relative position for each joint the center is calculated.

Joint center parameters

The joint center parameters are often gathered using stereo X-rays or MRI techniques and adjusting for variability within subjects using anthropometric parameters but only a few studies have been made for this purpose. In the 3Dkin program it is possible to use four different methods for determining the various joint centers:
bulletVaughan et. al. parameters
bulletCostum parameters
bulletCalculated parameters
bulletDigitized joint centers

Calculating or digitizing joint centers a separate file must be provided the 3Dkin program. The Marker configuration must be as following:
bulletMarker # 1 - Right toe
bulletMarker # 2 - Right ankle
bulletMarker # 3 - Right knee
bulletMarker # 4 - Right hip
bulletMarker # 5 - Left toe
bulletMarker # 6 - Left ankle
bulletMarker # 7 - Left knee
bulletMarker # 8 - Left hip

Linear aspects of segment motion

The linear aspects of segment motion is concentrated around the linear acceleration of the segment CM. The calculation is based on finite difference theory:

Angular aspects of segment motion

The relative orientation of a segment is defined by a position (X,Y,Z) and three angles (Euler angles). The position is obtained from marker trajectory. Using a reference system embedded into the segment three euler angles are calculated. The Euler angles are used for calculating angular velocity, acceleration and momentum.

Dynamics of joints

After all parameters are found (linear acceleration, angular acceleration, ground reaction forces and so on) the resultant net joint forces and moments can be calculated. As stated previously the model used is the free body diagram (FBD) where Newtons's second law of motion is applied to each segment. The law has both linear and angular aspects.


The final stage in the analysis of dynamic human motion is complete. The next step would be to calculate the tension of invidual muscles around the joints but the number of unknowns excedes the number of equations thus making it almost impossible.


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This page was last modified on 12/07/2008 at 22:47 PST. Copyright � 1994 - 2002, all rights reserved, Ariel Dynamics Inc. Please send your comments or feedback to or proceed to our feedback form. This page has been accessed many times since Dec 12, 2002. Our privacy policy is here.